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GR9277 #13
Problem
 GREPhysics.NET Official Solution Alternate Solutions
\prob{13}
Listed below are Maxwell's equations of electromagnetism. If magnetic monopoles exist, which of these equations would be INCORRECT?
I. Curl $\vec{H}=\vec{J}+\partial_t \vec{D}$
II. Curl $\vec{H}=\vec{J}+\partial_t \vec{D}$
III. Curl $\vec{H}=\vec{J}+\partial_t \vec{D}$
IV. Curl $\vec{H}=\vec{J}+\partial_t \vec{D}$

1. IV only
2. I and II
3. I and III
4. II and IV
5. III and IV

Electromagnetism$\Rightarrow$}Maxwell's Equations

Magnetic monopoles remain a likeable (even lovable) theoretical construct because of their ability to perfectly symmetrize Maxwell's equations. Since the curl term has an electric current, the other curl term should have a magnetic current. ($\nabla \cdot B \neq 0$ is taken to be obvious in presence of magnetic charge.) The answer is thus (D), and the revised equations are,

$\begin{eqnarray} \nabla \times H = J_e+\frac{\partial D}{\partial t}\\ \nabla \times E = -J_m-\frac{\partial B}{\partial t}\\ \nabla \cdot D = \rho_e\\ \nabla \cdot B = \rho_m.
\end{eqnarray}$

Alternate Solutions
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Danielperez123
2019-08-02 20:40:25
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ManuelR
2019-06-24 11:06:36
Yeah, you are right! D is the answer | https://www.michelsscreenandfence.com/
 danielsw986672019-07-31 13:06:29 Basing on Gauss\' law of magnetism and Faraday\'s law of induction, the answer is D.\r\nwww.clearviewwc.com/
Meggy12345
2019-06-21 05:48:50
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casseverhart13
2019-06-06 04:04:41
I tend to agree with that. Tree Solutions Winter Garden
patsm00re18
2019-06-06 02:52:41
 danielsw986672019-08-12 10:55:45 It was derived from the two laws: Gauss and Faraday. social security card application
Chris889
2019-04-04 13:55:38
Gosh, this is a lot to take. Can you explain in detail why D is the answer?\r\nChris | atlanta seo
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techblaster
2018-08-19 15:46:08
solidstate
2011-10-24 21:11:18
Isn't there TYPO in the question???
ramparts
2009-08-09 17:13:54
Even if you don't know exactly how the equations would change with monopoles, if you know that monopoles symmetrize the equations (by making some terms not 0), just compare like equations and see which ones are missing pieces. Eqn II is like Eqn I but without the J, and Eqn IV is like Eqn III but without the rho.
hoyas08
2007-12-26 16:45:26
The choices should be:

I. Curl H = J + ∂D/∂t
II. Curl E = -∂B/∂t
III. div D = ρ
IV. div B = 0

I think the answer is still D with these choices.
bootstrap
2007-04-05 19:14:29
All 4 of the curls in the question are exactly the same.
bootstrap
2007-04-05 19:14:20
All 4 of the curls in the question are exactly the same.
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LaTeX syntax supported through dollar sign wrappers $, ex.,$\alpha^2_0$produces $\alpha^2_0$. type this... to get...$\int_0^\infty$$\int_0^\infty$$\partial$$\partial$$\Rightarrow$$\Rightarrow$$\ddot{x},\dot{x}$$\ddot{x},\dot{x}$$\sqrt{z}$$\sqrt{z}$$\langle my \rangle$$\langle my \rangle$$\left( abacadabra \right)_{me}$$\left( abacadabra \right)_{me}$$\vec{E}$$\vec{E}$$\frac{a}{b}\$ $\frac{a}{b}$